Related papers: Algebraic Structure Discovery for Real World Combi…

Structural topology optimization (TO) is central to engineering design but remains computationally intensive due to complex physics and hard constraints. Existing deep-learning methods are limited to fixed square grids, a few hand-coded…

Reinforcement learning-based methods for constructing solutions to combinatorial optimization problems are rapidly approaching the performance of human-designed algorithms. To further narrow the gap, learning-based approaches must…

We reformulate the problem of modularity maximization over the set of partitions of a network as a conic optimization problem over the completely positive cone, converting it from a combinatorial optimization problem to a convex continuous…

Using machine learning to solve combinatorial optimization (CO) problems is challenging, especially when the data is unlabeled. This work proposes an unsupervised learning framework for CO problems. Our framework follows a standard…

Biclustering, also known as co-clustering or two-way clustering, simultaneously partitions the rows and columns of a data matrix to reveal submatrices with coherent patterns. Incorporating background knowledge into clustering to enhance…

To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…

Complex analyses involving multiple, dependent random quantities often lead to graphical models - a set of nodes denoting variables of interest, and corresponding edges denoting statistical interactions between nodes. To develop statistical…

This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic…

We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…

This article introduces a new physics-guided Machine Learning framework, with which we solve the generally non-invertible, ill-conditioned problems through an analytical approach and constrain the solution to the approximate inverse with…

In the majority of molecular optimization tasks, predictive machine learning (ML) models are limited due to the unavailability and cost of generating big experimental datasets on the specific task. To circumvent this limitation, ML models…

This paper investigates how the compositional structure of neural networks shapes their optimization landscape and training dynamics. We analyze the gradient flow associated with overparameterized optimization problems, which can be…

While algebraic derivations establish theoretical limits for quantum cloning, practical implementations require explicit operator representations that are often unavailable analytically. We present a computational framework that…

Techniques from higher categories and higher-dimensional rewriting are becoming increasingly important for understanding the finer, computational properties of higher algebraic theories that arise, among other fields, in quantum…

We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel…

We present a framework for computing the solution to Hamiltonian eigenproblems in a subspace defined by bit-strings sampled from a quantum computer. Hamiltonians are represented using an extended alphabet that includes projection and ladder…

Efficiently representing real world data in a succinct and parsimonious manner is of central importance in many fields. We present a generalized greedy pursuit framework, allowing us to efficiently solve structured matrix factorization…

The Grover search algorithm is one of the two key algorithms in the field of quantum computing, and hence it is of significant interest to describe it in the most efficient mathematical formalism. We show firstly, that Clifford's formalism…

For most algorithms dealing with sets of points in the plane, the only relevant information carried by the input is the combinatorial configuration of the points: the orientation of each triple of points in the set (clockwise,…

Quantum convolutional neural networks (QCNNs) represent a promising approach in quantum machine learning, paving new directions for both quantum and classical data analysis. This approach is particularly attractive due to the absence of the…